mathskool

fail: education of teachers

2009-05-19T11:37:00.000-07:00

Imagine you're teaching a class, and you give them a basic test to check that they know the minimal information they need to understand the subject. And 75% of your class flunks this test.

That's bad.

And that's what recently happened to a group of teaching candidates given a basic math test to evaluate their qualifications to be licensed educators.

If this situation happened with a group of students, I would not blame the students. Once failure reaches a certain ubiquity, it's clear that the expectations of the test are no long aligned with the accessibility of the information. Something has gone wrong with the education itself, not the students.

And so, in a highly cyclic fashion, we have an education problem that re-invents itself as the product of the previous generation proves itself poorly prepared to take the reins of the next.

How can we break out of the cycle? I suggest we begin by universally recognizing the problem. Follow up by providing motivation for smart people to go into teaching - make teaching a more respectable, reasonable, and decently-paying career (I'm saddened to realize that I can add "safety" to the list of things many teachers currently lack in their jobs). It's not easy, and I'm resisting the temptation to pontificate further on the tip of this iceberg.

Here's the short article about the abysmal candidate performance:

http://www.thebostonchannel.com/asseenon5/19502822/detail.html

You might notice the sample math problem they show. Yes, it would probably be trick for many very young students, but frankly it's easy for anyone who knows a little math. If your job is not only to understand basic math, but to teach it, then questions like this are more than reasonable.

chocolate is good for math

2009-04-06T13:32:00.000-07:00

It's true!

A recent study revealed that consuming cocoa-derived flavanols (naturally occurring in chocolate products) helped subjects attain improved performance in simple mental math:

http://www.telegraph.co.uk/health/healthnews/5095760/Scientists-reveal-how-eating-chocolate-can-help-improve-your-maths.html

As a mathematician, I must note that what they were really studying is basically just arithmetic, so claiming chocolate helps with all math from this study is akin to saying you'd be a better poet simply because you're better at spelling. Maybe some correlation, but it's a stretch.

In case you don't want to give yourself another excuse to consume vast quantities of cocoa, here are a few other items (according to this website) which also contain flavanols: red apples, apricots, and green and black tea.

youtube edu

2009-03-27T11:09:00.001-07:00

Yesterday google announced the release of the youtube edu channel:

http://www.youtube.com/edu

This is a subset of youtube videos devoted to education, primarily for college students.

Clearly, this is a good idea. Education is evolving to work better with modern resources (ie the internet), and this is another step in the direction of connecting great teachers with motivated students.

If mathskool were a business competing with youtube edu, this would concern me greatly :) But it has always been a key element of mathskool that it is a completely free and open service. If youtube makes a better service, it simply raises the standard. I plan to continue contributing to mathskool in my free time, in the hopes that any new features will be useful to students, and at very least encourage others to consider similar ideas or improvements. And the videos have always been hosted on youtube from the start, so that they still gain overall exposure and continue to help students through either site.

It's also important to note that youtube edu is focused on a different audience (college level), whereas mathskool is focused on middle/high school. In addition, the culture of youtube is less interactive than the vision of mathskool. Of course, youtube already has a great community of users, which is an as-yet-unmet prerequisite for a truly interactive mathskool community.

Keep up the good work, open educators!

Thoughts on math curriculum

2009-02-28T15:10:00.000-08:00

This article is written concerning the national Australian math curriculum, but I very much appreciate the author's perspective on how we think about math education:

What do I want from a national curriculum? I want a dodecahedron in every classroom, and beautiful diagrams to ponder. I want students to know why there are infinitely many prime numbers, and for them to realise no one knows about twin-primes. I want them to know what the golden mean is, and why it is irrational, and why we care. I want pattern and play and beauty. And I want the times tables.
Is teaching any of the above useful? It is exactly as useful as teaching Harry Potter and Shakespeare.

Ok - I actually think some of the most beautiful mathematics happens to also be very useful - in this regard, I don't totally agree with the author (Marty Ross). Understanding the structure of the primes and related ideas gives us many cryptographic tools, for example. Understanding the meaning of irrational or transcendental numbers lets us know when certain things are impossible - we won't waste our time searching for an algorithm to square the circle (using the traditional construction tools, that is). And that just scratches the surface.

But the analogy to popular and influential works - Harry Potter and Shakespeare - is something I think many educators and students don't recognize. It is obvious that the large majority of careers don't rely on a profound understanding of Shakespeare, and yet we feel that an education without such crucial literary components is incomplete. Why do so many people seem to consider the beauty and value of the world knowledge of math to be inferior? Some may argue that math lacks the cultural saturation of great works of art, and I would have to agree. And yet, math is everywhere, and not because we write stories about it, but because it describes the raw logic and flow of the world around us. To borrow a phrase from Robert Osserman, math is the poetry of the universe.

uservoice

2009-01-27T11:32:00.000-08:00

Who knows best about what's good and bad about the present and potential future of mathskool.com? You, the users!

That's why I just added a link from the top of the mathskool.com headers to our own uservoice page. This is a very nice user feedback system for collecting and discussing ideas and bug reports. Every time you have an idea, type it into uservoice, and they automatically search for similar ideas. This way you avoid duplicate ideas, and you can vote in the main thread representing your idea. As the mathskool web builder, I can also provide plenty of feedback on these ideas - marking things as planned, started, completed, or not going to implement in some cases. It's a nice interface, and I'm glad I can give users a very friendly way to express their thoughts on the site.

one in a million?

2009-01-24T05:15:00.000-08:00

This article:

http://www.kansascity.com/450/story/996042.html

recently claimed that the odds of the same pick-3 lottery ticket happening two days in a row - which did happen this past Monday and Tuesday - are one-in-a-million, so that it was a rather surprising occurrence. The choices allow ten numbers in each of three places, and order matters. So there are 1000 choices of ticket. But that means, whatever yesterday's winning numbers were, the odds they're the same today is 1 in a 1000, not 1 in a million. We'd actually expect this to happen about once in three years - not such a wild coincidence after all.

The fact that this article was published at all is a little scary to me. This is very basic probability theory - even if math is a journalist's weak point, I would imagine you could double-check such a key fact with someone else who knew their stuff. In an ideal world, responsible members of the media would have at least a better intuition for something like this.

Of course, I'm not so worried about trivial inaccuracies in novelty news, so much as I am about a general lack of educated reporting - the kind of thing that has lead many folks (at least in the US) to doubt the legitimacy or human-influence on global warming, for example. This is an area on which the scientific community has been in virtual consensus for many years, contrary to the impression you might receive from certain media outlets. Any good disseminator of knowledge cites their sources, so I'll back that up with a quote from the Doran/Zimmerman 2009 report on scientific opinion of global warming:

It seems that the debate on the authenticity of global warming and the role played by human activity is largely nonexistent among those who understand the nuances and scientific basis of long-term climate processes.

If you're curious, there's more on this wikipedia page.

math is the best!

2009-01-12T07:19:00.001-08:00

A recent article by a career expert at careercast.com ranks mathematician as the best overall job. Cool.

I sometimes forget how much nicer it is to be a mathematician / programmer than some of the lower-ranked alternatives, such as taxi driver or lumberjack.

Unfortunately, I'm not sure this article could effectively change a lot of young students' minds about how much they like math. If you ask a kid if they'd rather do some math or take a chainsaw to a tree, I think most would choose the chainsaw. It seems to reduce to the more profound problem of making life choices in the context of youth - your first glimpses of the various options (such as careers) can be fleeting and misleading, and the school culture of your peers adds pressure to base decisions on status more than intrinsic merit.

Here's a Wall-Street Journal article about the jobs rankings:

http://online.wsj.com/article/SB123119236117055127.html

launched!

2009-01-01T18:11:00.000-08:00

I'm very happy to announce that the alpha version of mathskool has just launched! When you go directly to mathskool.com, you'll now see the main page.

The "alpha version" means we're still in early testing, and several big features - such as search - are still in the works.

I'm sure there are a few bugs already, and new ideas coming in, so I'll soon be adding a uservoice.com link to help users file bug reports and feature requests.

This blog will continue to catalog new features and other mathskooly news - available as always at mathskool.com/blog.

Now go check out the site!

Purdue might require 4 years of HS math for new students

2008-12-30T09:04:00.001-08:00

It makes sense for college admissions to require that some incoming students have a better math background, because this has been shown to correlate with how well the students will do, and their chances of actually graduating. You could argue that it seems unfair for a college to require students to complete more math than their high school does, but it's well known that completing the bare minimum at any high school in no way guarantees you admission into any good college. In fact, adding requirements at the college level gives students more flexibility - if they want to get a BA in something non-mathy, they might get away with less math - let that be their choice.

Side note: I find it interesting that articles like this often mention that more math background correlates with better college performance (anyone know of a primary reference for that fact?) Even if teachers find it difficult to articulate exactly why math is good for students, this is a big hint.

Here's the Purdue article:

http://www.indystar.com/article/20081230/LOCAL/812300375

MIT open courseware - very cool

2008-12-22T20:32:00.000-08:00

Yesterday I was browsing MIT's open courseware pages:

http://ocw.mit.edu/

The program offers a variety of very high-quality online course materials for undergraduate- and graduate-level classes. In many cases, they also have videos hosted on youtube.

I watched one class on practically solving large sparse linear equations with an introduction to partial differential equations, taught by Gilbert Strang - it was extremely well-taught! If you want to check out Prof Strang's Linear Algebra courses, search for "18.06" on youtube. Here's the first lecture in that series:

http://www.youtube.com/watch?v=gVMRuLH6FdQ

This stuff strongly suggests that online learning can very well work for more advanced materials. Personally, I'm guessing that a bottleneck for online learning (besides internet access of course) is the maturity of the students, so that online education resources actually become more effective as the intended audience gets older.

teachertube

2008-12-20T20:34:00.000-08:00

A few days ago someone pointed me to teachertube, basically a version of youtube which is specific to educational videos. This has a lot of overlap with mathskool, although there are a few significant differences - in particular, mathskool will be much more focused in topic (only math stuff), and will supplement the videos with a rated question/answer system, along with other optional supporting materials.

I'm excited to see that teachertube has already gained a respectable library of videos in a variety of subject areas. This gives me hope that teachers are willing and able to contribute their time to a free online learning resource, and that there is strong potential to build an evolving math education community around mathskool.

Algebra video playlist

2008-12-17T21:14:00.000-08:00

These six videos offer a quick introduction to the beginning ideas of algebra. I hope to use something like playlists, in the form of "previous" and "next" links, to tie together a string of videos that can be watched in order. The difference is that you can have multiple "next" videos, so that you can choose to elaborate on the parts of the video you care about the most. For example, imagine learning about Pascal's triangle for the first time. From there, you could learn more about similar types of sequences, about other things you can do with binomial coefficients, about proofs by induction, or about how it relates to fractals like the Sierpinski triangle.

Terence Tao on multiple choice tests

2008-12-16T17:18:00.000-08:00

Just a quick link today to a blog post by Terry Tao (a pretty good mathematician). He recently posted some thoughts on the utility of multiple choice questions.

I remember, from my teaching days at NYU, that many undergrads think that "multiple choice" means "easy". I felt slightly guilty in showing them otherwise. I think Mr. Tao's example questions help illustrate some of the possibilities.

graphic novel / manga learning

2008-12-15T18:38:00.000-08:00

When I was a kid, I learned a lot from a series of books by Larry Gonick called "The Cartoon Guide to X" where X could be anything from physics or genetics to computers or the history of the universe. The thing about these engaging, fun-to-read books is that they really conveyed the key ideas and unifying themes behind each subject - at least as much as any text could in a single book. These aren't comic books.

Reading the good math/bad math blog (also by a mathie who's been at google for a little bit), I saw this review on The Manga Guide to Statistics. Apparently it's good. A quick search on amazon reveals that there are even more of these manga guides around. If I had kids, I'd probably buy them these books. Very cool!

Work in progress

2008-12-14T20:50:00.001-08:00

Here's the state of the main video-watching page so far - this is a static image of a php page that's half-way done:

(You can compare this to the paper mock from six days ago, if you're curious :)

pondering metaverse learning

2008-12-13T17:24:00.000-08:00

Reading through a few blogs of others interested in math education, I came across the pioneering efforts of the cool cat teacher to promote online citizenship in a 3d web world (something like second life) among her students. In particular, this blog post outlines some of her key thoughts on the idea. I'll copy of her list of possible advantages teachers can promote for students who learn through an online 3d world:

You can go places that can't be visited today.
You can overcome stereotypes.
Student collaboration
Project-based learning possibilities
Role playing [think: trying out possible future careers]
Potential for group synergies
Storage, legacy, and global audience
Scenario simulation [think: virtually perform dangerous chemistry lab experiments]
Digital storytelling

I don't see mathskool starting out with a major role in the 3d web, but I think these are great ideas towards the evolution of technology and teaching. I expect that many of these possibilities can't come to full fruition until some aspects of the 3d web have improved, such as better bandwidth for the average student, better graphics processors in the average computer (that is moving along nicely, thanks partially to video games :), better user interfaces for online interaction (right now I feel that there's a too-huge gap between how natural it feels to "be" online vs reality), and better systems to enable safe yet open environments for young people.

The Khan Academy and other mathy youtubers

2008-12-12T17:38:00.000-08:00

Yesterday the Associated Press published an article about students using youtube videos to help study up on classes on their own time. In particular, they mention a series of videos uploaded by Salman Khan, who has (at my latest check) well over 600 videos on youtube, many of which are math lessons.

The videos seem very friendly, and are easy to watch. I noticed that he uses a different method of recording his lessons - instead of a video of a chalkboard or a whiteboard, he simply uses a video capture of a paint-like program, with a voiceover to explain what he's writing. The result is pretty clear text (on youtube), although it is always harder to write neatly with a mouse than directly by hand.

I'm very happy to see that this idea already has some momentum, and that others are happy to contribute their lessons without any obvious reward (besides good karma and feeling good about what you're doing, of course :). I hope I can integrate work like this into the initial offerings of mathskool.

a student perspective

2008-12-11T14:08:00.000-08:00

I am extremely tempted to analyze this perspective of math education. But, really, this student speaks for herself.

math teacher supply and demand

2008-12-10T14:57:00.000-08:00

The Center for the Future of Teaching & Learning released a report today about the status of California's teachers, comparing statistics of teacher credentials, experience, and student performance. The study makes several points; for mathskool, I found it most interesting that around one third of California's middle school algebra teachers are considered "underprepared", meaning that they either lack experience (<= 2 years) or that they do not possess full credentials to teach math (see appendix B of the full report - link below - for more details on what counts as "underprepared").

The downward trend in this graph is nice, but having 1/3rd of our students taught middle school math by underprepared teachers sounds a bit scary.

I hate to see hard-working teachers faced with labels that might be considered as demeaning their efforts. Every teacher has to start off as a newbie - this can't count against them. And I believe that every teacher genuinely wants to provide the best education possible for their students, regardless of their credential level.

There are some constructive lessons we can learn from this data. It seems clear that we need more teachers than are available. Relating this to the TIMMS report, it comes to mind that Asian cultures generally hold teachers in much higher regard than we do our American educators. As a graduate student in mathematics, I strongly felt pressure to avoid educational positions, as these are viewed as a "way out" of doing "real math" -- at least, that is the perception I had. And the percentage of our national budget which is allocated to education is a fraction of that we spend on defense. All of this adds up to a discouraging environment for potential future educators. If you're good at something, why teach it for less respect and less money, when you can have a better life working in industry, or at least in higher education (college or other research-friendly places) ?

I don't think there is a silver bullet toward improving the state of our education system, but I do believe that a general agreement in attitude among a strong community of educators can be the start of a better system - especially with a little political support. It is my hope that mathskool can play a role in empowering such a teacher community, by giving great, experienced teachers a stronger voice, new teachers a source of guidance, and our students an effective new resource for learning which is at once easy-to-use, non-intimidating, and responsive to their feedback and desire to understand.

Information on the report:

TIMMS: good work - now let's do better

2008-12-09T15:10:00.000-08:00

The latest TIMMS (Trends in International Mathematics and Science Study) report came out today, with data from 4th and 8th grade science and math student scores from many countries throughout the world. TIMMS is directed by the International Study Center at Boston College. Every four years, they gather data about how well students perform, on average, in each of several different countries (and some individual US states) in some key areas within math and science.

I'm going to focus on 8th grade math performance results, since that's the most pertinent to mathskool. Based on this table, the average US student score (8th grade math) was 508. This ranks 9th in the world, and is pretty far behind several Asian countries lead by Taipei with 598. It's slightly above the international average of 500.

There are a few ways to look at this data. Some, such as Sam Dillon from the New York Times, are focusing on the fact that our scores have improved a bit since 2003 (cf. this table). Others, such as Maria Glod, Washington Post, point out that we're still way behind the Asian leaders in education.

I'd like to congratulate the hard work and improved results of our teachers and students. We're headed in the right direction. But at the same time, it would be great to see our students perform at a more competitive level. If we saw our average Olympic game performance was 9th in the world, we wouldn't say "hey, it's still top 10!" We would push for the gold, and if I can be any part of that, then I'd like to contribute.

Below is a chart comparing the 2007 TIMMS scores of the top 11 countries versus national GDP per capita, as a sort of measure of each country's wealth. I've circled South Korea and Taipei as doing particularly well, and the US and England as having room for improvement, especially considering our per capita GDP.

I got the GDP data from this wikipedia page, which credits the data to the CIA.

lessons from video #2

2008-12-08T17:19:00.000-08:00

There will probably be a few improvements over time as I figure out how to produce better math lesson videos for the site. Some tips:

Write big! I'm aiming for a letter height that would allow me to have about 7 lines from top to bottom of the video view. Some quick testing seems to show that trying to fit 8 or more lines in results in text that is too small.
Don't use fine point markers - use the big ones - also because readability on youtube videos is challenging.
Record in short takes, say 1 minute or so each. This allows for easier re-do's when something goes skewampus. I also step out of the frame at the end of each take, and back in at the start, to preserve continuity.
Before you start recording, check that the video frame includes the entire area (such as a whiteboard or chalk board) that you want to include.
Check for distracting lighting elements, such as reflections, glare, or shadows.
Be aware of any branding or slogans on your clothes. I'm wearing a google jacket here, which is ok, but in the future I plan to wear plain colors to avoid any mistaken associations.

The second video (shorter, more readable than the quadratic formula one):

paper mocks

2008-12-08T14:25:00.000-08:00

Don't you love the amazing top quality design work of aesthetically-pleasing companies like Apple? Don't you wish all websites could implement easy-to-use, nice-looking interfaces that worked on basically every web browser? Me too.

Unfortunately, the nice round figure that is the mathskool budget does not allow for fancy design tools. Hence I present the first slightly-low-tech mock for a video-watching page on mathskool (click to bigify):

The idea is that users can search or browse for videos they'd like to see from the frontpage, and from there arrive at a video-watching page which clearly associates the given math video with supplementary materials, such as links to subsequent videos to watch, other sites exploring the topic, or a PDF of worked example problems. From the same page, users can also view questions and answers based on the topic of the video (there might be more than one video per topic), rate the video or the related questions, or bookmark it as a favorite for easy reference.

first video: the quadratic formula

2008-12-07T17:35:00.000-08:00

The first video is up on youtube! It's a two-parter on the quadratic formula:

QUADRATIC_FORMULA_VIDEO

I learned a few things putting this together:

youtube currently supports higher quality video than google video, but with a 10 minute limit
google video allows longer videos, but the quality is not good enough for typical slides or board writing
it takes a while to compress and upload videos!

Despite the 10 minute limit being cumbersome, I think we might be able to use this as a constructive constraint, in that it enforces short videos which students are more likely to actually watch. I've seen first-hand how challenging it can be to compress a certain amount of material into a short time-limit -- my first video is about 20 minutes! I'll have to work on this for my own video contributions.

tips for teachers creating videos

2008-12-06T19:07:00.000-08:00

Here are a few tips for teachers who are interested in contributing videos to the initial offering of mathskool:

The idea is to create a brief (say, 10 min or less) presentation about a single, focused topic. Some students are self-motivated, but anyone is more likely to watch a <10 min video that covers the one part they want to learn or review instead of a comprehensive 40 min video, part of which may be redundant to the student.

Once mathskool is set up, it will support sections for various types of supplementary materials for each video. The design will prominently show links to "next" videos that the student may want to explore immediately after watching the current video; you may also indicate "prerequisite" videos in case you assume some knowledge in your lesson. This is meant to encourage teachers to break down longer lessons into smaller pieces, and then string those pieces together with links so that students can easily follow.

What's a good outline for a single video? I don't want to constrain the creativity of the teachers - I can imagine many different types of information being expressed in many different ways. But, in case it helps, here are some possible outlines for short lessons, based on the type of lesson at hand.

Introducing a new method of solution (e.g. solving quadratic equations)
- Define terms and clearly state the general question to answer
- Give a concrete example of the question
- Explicitly state the general solution, and how to apply it
- Solve one or more concrete examples
Introducing a new definition or concept (e.g. the idea of a function)
- You could frame the concept in terms of how it is useful - what problem is made easier using this idea?
- Clearly and explicitly define the new concept
- Give several examples and non-examples
- If appropriate, solve a problem using the new concept
Working out examples
- Very briefly review the idea being illustrated by these examples
- For each example, start by clearly stating the problem to solve
- Work through each step carefully, writing down and saying aloud the process
- Write out the final solution
- If appropriate, explain how this demonstrates the idea being illustrated

mathskool headquarters

2008-12-05T15:45:00.000-08:00

As of today, mathskool now has an official headquarters. With a little help from Ikea, Target, Wal-mart and Fry's, the office is now fully equipped with all the essential tools of any productivity center:

bookshelf with some math books
pen/pencil holder and notepads
whiteboards
docking station for the macbook
mini-fridge
ramen noodles

the stuff:

construction:

Kepler (the dog) offers moral support:

done!